Here's a question ~

Two lines passing through the point (2 , 3) intersect each other at an angle of 60° . If slope of one line is 2, then find the equation of the other line ~

note : there are two possible slopes !

Need Proper Explanation ~​

Answers

Answer 1

Answer:

[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]

Step-by-step explanation:

It is given that –

Slope of the first line is–

[tex]\sf\longmapsto \: m_{1} = 2[/tex]

Let,

the slope of the Another line be –

[tex]\sf\longmapsto \: m _{2}[/tex]

Now,

The angle between the two lines is 60°.

Let's start solving!

[tex]\sf\longmapsto \: \tan(60°) | \frac{ m_{1} - m_ {2} }{1 + m_{1} m_ {2}} | [/tex]

[tex]\sf\longmapsto \: \sqrt{3} = | \frac{2 -m_{2} }{1 + 2m_{2}} | [/tex]

[tex]\sf\longmapsto \: \sqrt{3} = ± \: \: ( \frac{2 -m_{2} }{1 + 2m_{2}} )[/tex]

[tex]\sf\longmapsto \: \sqrt{3} = \frac{2 -m_{2} }{1 + 2m_{2}} [/tex]

[tex]\sf\longmapsto \: \sqrt{3} (1 + 2m_{2}) = 2 - m_{2}[/tex]

[tex]\sf\longmapsto \: \sqrt{3} + 2 \sqrt{3} m_{2} + m_{2} = 2[/tex]

[tex]\sf\longmapsto \: m_{2} = \frac{2 - \sqrt{3} }{(2 \sqrt{3} + 1) } [/tex]

The equation of line passing through point (2,3) and having a slope of –

[tex]\sf\longmapsto \: m_{2} = \frac{(2 - \sqrt{3} )}{2 \sqrt{3} + 1 } [/tex]

is–

[tex]\sf\longmapsto \: (y - 3) = \frac{2 - \sqrt{3} }{2 \sqrt{3} + 1 } (x - 2)[/tex]

[tex]\sf\longmapsto \: ( 2\sqrt{3} + 1)y - 3(2 \sqrt{3} + 1) = (2 - \sqrt{3} )x - 2(2 - \sqrt{3} [/tex]

[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]

Hence the equation of the other line is -

[tex]\sf\longmapsto \: ( \sqrt{3} - 2)x + (2 \sqrt{3 } + 1)y = - 1 + 8 \sqrt{3} [/tex]


Related Questions

The inverse of Fx) is a function.
True or False

Answers

It is true because it passes the horizontal line test

Answer:

The answer would be true

Step-by-step explanation:

Since there is only one y for every value  of x and only one x for every value of y, both this graph and it's inverse would both be functions.


Here are the two triangles from the previous screen,
along with the length you entered for XY.
What is the slope of the line?
[_________] Submit and Explain

Answers

Answer:

the slope is 1/2

Step-by-step explanation:

I picked two points (the two from the purple triangle) and I did the rise over run. The rise was 3 and the run was 6 so the slope is 3/6 but when you simplify it, it goes down to 1/2

Mr. Garcia wants to package 16 math books and
20 science books into boxes. Each box will have the
same number of each type of book, with none left
over. What is the greatest number of books he can
put in each box? How many boxes are needed?

Answers

Answer:

four boxes are needed, greatest number 9??

Step-by-step explanation:

16 math and 20 science

4           5

4           5

4           5

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you can divide both by 4

hope that helps

Schumer Box How To Read The Fine Print

Answers

Answer:

what'd you mean?

Step-by-step explanation:

How many solutions does this system have?
y = 5x + 6
y – 5x = 7

A. no solutions
B. 1 solution
C. 2 solutions
D. infinitely many solutions

Answers

Answer:

No Solutions

Step-by-step explanation:

The two lines never intersect

Answer:

A

Step-by-step explanation:

y = 5x + 6 → (1)

y - 5x = 7 ( add 5x to both sides )

y = 5x + 7 → (2)

Substitute y = 5x + 7 into (1)

5x + 7 = 5x + 6 ( subtract 7 from both sides )

5x = 5x - 1 ( subtract 5x from both sides )

0 = - 1 ← is False

This indicates the system has no solution

Which ordered pair is a solution to the system of linear equation? 2x+ 3y=6
-3x+5y=10

Answers

Answer:

x = (-2)y = 2

Step-by-step explanation:

2x + 3y = 6________( 1 )

-3x + 5y = 10_______( 2 )

( 1 ) × 3 ---- 6x + 9y = 18_____( 3 )

( 2 ) × 2 ---- -6x + 10y = 20_____( 4 )

[tex](4) + (3) \\ 6x + 9y + ( - 6x + 10y) = 20 - 18 \\ 6x + 9y - 6x - 10y = 2 \\ y = 2[/tex]

y = 2 ,

[tex]2x + 3y = 6 \\ 2x + 3(2) = 2 \\ 2x + 6 = 2 \\ 2x = 2 - 6 \\ 2x = - 4 \\x = \frac{ - 4}{2} \\ x = ( - 2) \\ [/tex]

can anyone help me with this?

Answers

Answer:

Below.

Step-by-step explanation:

7)  c^2 = a^2 + b^2

15^2 = 11^2 + b^2

b^2 = 225 - 121 = 104

b = √104

= √4√26

= 2√26.m

8). 4^2 = a^2 + (√6)^2

a^2 = 16 - 6

a^2 = 10

a =  √10.

Use the quadratic formula to solve x2 – 5x - 2 = 0.

Answers

Answer:

• The quadratic formular is as below:

[tex]{ \boxed{ \rm{x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} }}}[/tex]

• Basing on our equation given, x² - 5x - 2 = 0;

a → 1b → -5c → -2

[tex]{ \rm{x = \frac{ - ( - 5) \pm \sqrt{ {( - 5)}^{2} - (4 \times 1 \times - 2) } }{(2 \times 1)} }} \\ \\ { \rm{x = \frac{5 \pm \sqrt{33} }{2} }} [/tex]

• Therefore;

[tex]{ \boxed{ \rm{x = \frac{5 + \sqrt{33} }{2} }}}{ \rm{ \: \: or \: \: }}{ \boxed{ \rm{x = \frac{5 - \sqrt{33} }{2} }}} \\ \\ { \boxed{ \boxed{ \rm{x = 5.37 \: \: or \: \: - 0.37}}}}[/tex]

x + y 6x - 4y - 2 simplified?

Answers

Step-by-step explanation:

X + Y + 6X - 4Y - 2 would be 7x - 3y -2

:) hope this helped let me know if you need more help! :)

>> Algebra

____________

[tex] \: [/tex]

x + y + 6x - 4y - 2 = ...

= (1x + 6x) + (1y - 4y) + (-2)

= 7x - 3y - 2

What is the midpoint of this segment

Answers

Answer:

(1,1)

Step-by-step explanation:

(ii) Explain why a+b+c= 235°
This is a cornet maths question. How do I solve it

Answers

Answer:

Where is the image?

Step-by-step explanation:

Tell me in comments

The equation a + b + c = 235 is true because a = c = 55° and b = 125°

How to prove that a + b + c = 235?

The angle a and 125° are on the same straight line.

So, we have:

a + 125° = 180°

Subtract 125 from both sides

a = 55°

The angle b and 125° are vertical angles

So, we have:

b = 125°

The angle a and angle a are vertical angles

So, we have:

c = a

This gives

c = 55°

Add the three angles

a + b + c = 55° + 125° + 55°

Evaluate the sum

a + b + c = 235°

Hence, it is true that a + b + c = 235°

Read more about vertical angles at:

https://brainly.com/question/14362353

m/5=3(2m+1) verbal expression

Answers

Answer:

m = -15/29

Step-by-step explanation:

1) Distribute

[tex]\frac{m}{5} =6m+3[/tex]

2) Subtract 6m from both sides of the equation

[tex]\frac{m}{5} -6m=6m+3-6m[/tex]

3) Simplify

a. Find common denominator

[tex]\frac{m}{5} +\frac{5(-6)m}{5} =6m+3-6m[/tex]

b. Combine fractions with common denominator

[tex]\frac{m+5(-6)m}{5} =6m+3-6m[/tex]

c. Multiply the numbers

[tex]\frac{m-30m}{5} =6m+3-6m[/tex]

d. Combine like terms

[tex]\frac{-29m}{5} =6m+3-6m[/tex]

e. Combine like terms

[tex]\frac{-29m}{5} =3[/tex]

4) Multiply all terms by the same value to eliminate fraction denominators

[tex]5 *\frac{-29m}{5} =5*3[/tex]

5) Cancel multiplied terms that are in the denominator

[tex]-29m=5*3[/tex]

6) Multiply the numbers

[tex]-29m=15[/tex]

7) Divide both sides of the equation by the same term

[tex]\frac{-29m}{29} =\frac{15}{-29}[/tex]

8) Simplify

a. Cancel terms that are in both the numerator and denominator

[tex]m=\frac{15}{-29}[/tex]

b. Divide the numbers

[tex]m=-\frac{15}{29}[/tex]

If a jar contains 3 blueberry, 4 ginger, 1 green, and 6 regular tea bags, what is the probability that a regular tea bag will be pulled from the jar? Answers must be in simplest form.

Answers

I love blueberries so 10+y is not right answer

R.
Y.
12 cm
20 cm
13 cm

-
Find volume

Answers

Answer:

3120

Step-by-step explanation:

v=lxbxh

...........

Step-by-step explanation:

The volume = 12 × 13 × 20 = 3120

please give me a brainliest answer

Please help me with this!

Answers

Answer:

y=2x+3

Step-by-step explanation:

you should see how to get from one number to the next.

I noticed by multiplying an input by 2 then adding 3 I reach my output.

I would use this for each input to find that it would equal my output every time I used the rule

Which function is equivalent to g ( x ) = x 2 + 15 x - 54?

Answers

Answer:

g(x) = (x+18)(x-3)

Step-by-step explanation:

g(x) = x²+15x-54= x²+18x-3x+54= x(x+18) -3(x+18)g(x) = (x+18)(x-3)

on a sunny day liam decided to walk to his grandmother's house. After walking for a while at a rate of 3 mph, Liam realized that it might start raining, so he decided to take a taxi the rest of the way. The taxi traveled at a speed of 30mph. If he arrived 2 hours before he started, what distance did liam traveled by taxi?

Answers

The answer is ten. The formula for calculating speed is as follows:

Speed = distance × time. Knowing the distance and time units is required to calculate the speed units.

Explain about the speed?

A bicycle that travels 30 meters in two seconds, for example, is moving at a rate of 15 meters per second. The speed of an object in motion varies frequently (for example, a car may travel down a street at 50 km/h, then slow to 0 km/h, and then accelerate to 30 km/h).

The rate at which a distance changes over time is referred to as speed. It has a dimension of time and distance. As a result, the SI unit of speed is formed by combining the fundamental unit of time and the fundamental unit of distance. As a result, the SI unit of speed is the meter per second (m/s).

To learn more about speed refer to:

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carol's father was 24 years old when carol was born, now he is 4 times as old a carol how old is carol

Answers

Answer:

24 - 24 = 0 (carols age past tense)

24 x 4 = 96

96 - 24 = 72 (present tense)

carol is now 72 yr

AM I RIGHT PLEASE HELP!!!
Calculate the slope of a line that passes through the points (6, -12) and (15,-3).

Answers

Answer:

slope = 1

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (6, - 12 ) and (x₂, y₂ ) = (15, - 3 )

m = [tex]\frac{-3-(-12)}{15-6}[/tex] = [tex]\frac{-3+12}{9}[/tex] = [tex]\frac{9}{9}[/tex] = 1

Can someone tell me the answer to this

Answer choice D is incorrect

Answers

Answer:

A

Step-by-step explanation:

It's going to get smaller

asap po please thank you po!

Answers

Answer:

1 is correct, 100.

2 is 500, not 470. since we're rounding to the nearest hundred, we would look at the tens place and if it's higher than 5 then round up.

3 is correct.

4 is correct.

5 is correct.

6 is correct.

7 is correct.

8 is 290, not 300. like i said before, but in this case we're rounding t the nearest ten instead of hundred. but the same rules apply.

9 is correct.

and 10 is correct!

i think that you did pretty well on most of these, but remember the rounding rule.

15 cm
T
9.9 cm
12 cm

-
Find volume

Answers

Step-by-step explanation:

The volume = 15 × 4.2 × 9.9 = 623.7

please give me a brainliest answer

Which of these is a good conductor?
wood
silver
paper
air

Answers

Silver is an excellent conductor for heat.
the answer is silver

Para que con exactitud se pueda poner líquido en dos tambos de 60 y 90 litros, respectivamente, ¿Cuál es la capacidad máxima en litros que debe tener el recipiente a utilizar? *​

Answers

Answer:

No estoy muy seguro de esta pregunta principalmente porque tuve que traducirlo del español al inglés, pero creo que el toldo es de 120 litros. Avísame si me equivoco

Step-by-step explanation:

Esto se debe a que 60 litros es el máximo que puede aguantar el más pequeño por lo que para poner 60 litros en cada uno debes tener 120 litros en total.

Bertha read 21 books. Each book had 155 pages. How many pages did she read altogether? 465 pages
3,155 pages
3,355 pages
3,255 pages

Answers

21 x 155 = 3255
She read 3255 pages altogether.

Answer:

3,255 pages

Step-by-step explanation:

multiply 155 by 21

mathematics
Solve k - 120= 768 Find the value of k

Answers

Answer:

[tex]k - 120 = 768[/tex]

add 120 to both sides of the equation

[tex]k - 120 + 120 = 768 + 120[/tex]

120 on the left hand side of the equation cancels therefore isolating the variable, k

[tex]k = 888[/tex]

Please help me!!!!! THIS IS LATE NEED HELP!!!! Just a head's up the graph x and y axis goes by 2 not 1.
Find two points from this graph and then determine the slope.

Answers

First point (4,2) , (6,5)
slop = y2-y1/x2-x1
=5-2/6-4
Slop= 3/2

help me with this please

Answers

Answer: 65

Step-by-step explanation:

What is the formula of speed?

Answers

Answer:

d/t

D= Distance

T= Time

Step-by-step explanation:

[tex]▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪[/tex]

The formula to find average speed ~

[tex] \mathrm{ \dfrac{total \: \: distance \: \: covered}{total \: \: time \: \: taken} }[/tex]

Formula for Instantaneous speed ~

[tex] \dfrac{ds}{dt} [/tex]

where,

s represents distance covered

t represents time

It's derivative of distance with respect to time ~

hope it helps !

Anyone, please answer this question

Answers

Answer:

The answer is A.

Step-by-step explanation:

they equal the same amount

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